Discretization of interior point methods for state constrained elliptic optimal control problems: optimal error estimates and parameter adjustment

被引：17

作者：

Hinze, Michael ^{[1
]}

Schiela, Anton ^{[2
]}

机构：

[1] Univ Hamburg, D-20146 Hamburg, Germany

[2] Konrad Zuse Zentrum Berlin, D-14195 Berlin, Germany

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2011年 / 48卷 / 03期

关键词：

Elliptic optimal control problem; Error estimates; Interior point method; Pointwise state constraints; FINITE-ELEMENT APPROXIMATION; DIRICHLET PROBLEM; MINIMIZATION; CONVERGENCE; EQUATIONS;

D O I：

10.1007/s10589-009-9278-x

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

An adjustment scheme for the relaxation parameter of interior point approaches to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method is based on error estimates of an associated finite element discretization of the relaxed problems and optimally selects the relaxation parameter in dependence on the mesh size of discretization. The finite element analysis for the relaxed problems is carried out and a numerical example is presented which confirms our analytical findings.

引用

页码：581 / 600

页数：20

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